Abstract:

An Adaptive-Subspace Self-Organizing Map (ASSOM) can
learn a set of ordered linear subspaces which correspond to invariant
classes. However the basic ASSOMcannot properly learn linear manifolds
that are shifted away from the origin of the input space. In this paper, we
propose an improvement on ASSOM to amend this deficiency. The new
network, named AOSSOM for Adaptive Offset Subspace Self-Organizing
Map, minimizes a projection error function in a gradient-descent fashion.
In each learning step, the winning module and its neighbors update
their offset vectors and basis vectors of the target manifolds towards the
negative gradient of the error function. We show by experiments that
the AOSSOM can learn clusters aligned on linear manifolds shifted away
from the origin and separate them accordingly. The proposed AOSSOM
is applied to handwritten digit recognition and shows promising results.